Note-This will be my personal views on the concerned topics as an explorer of Data Sciences and Strategy Professional.

What are must learn programming language as an analytics professional?

Most used statistical modeling programming languages are R, Python and SAS

Any book that I should read as business professional to know more about analytics?

You can try "Super Cruncher" by Ian Ayres.., I loved reading this books around a decade back..

Any Statistics book that I should use to refresh my fundamentals?

I loved reading a very thin book in statistics by PL Meyer - Introductory Probability and Statistical Application

What are most used statistical algorithms in Industry?

There are many business problems that fall in the category of event prediction like default in credit card, Loan or any credit driven business, propensity to purchase, Cross sell and upsell opportunity.. These kind of event classification problems are very generic in day to day analysts life.., hence I would recommend you to must learn techniques like Logistics Regression, Decision Tree, Neural Network classification models.. you can explore more